Acoustic Luneburg lens (ALL) is a spherically/circularly symmetric gradient refractive index lens, whose index varies smoothly from the outer surface to the centre. The variation of the index can be achieved via the changing of filling ratio of unit cells or varying the structural thickness based on specific governing equations. The fundamental principles were used to explain the acoustic wave propagation in such inhomogeneous media, and to design different types of ALL. This review will describe the fundamental theories of ALL, introduce different types of ALL, and discuss extensive applications of ALL, which have been exploited for the manipulation and control of both acoustic and elastic waves.

声学 Luneburg 透镜 (ALL) 是一种球形/圆形对称梯度折射率透镜，其折射率从外表面到中心平滑变化。该指数的变化可以通过改变晶胞的填充率或基于特定的控制方程改变结构厚度来实现。基本原理用于解释声波在这种非均匀介质中的传播，并设计不同类型的 ALL。这篇综述将描述 ALL 的基本理论，介绍不同类型的 ALL，并讨论 ALL 的广泛应用，这些应用已被用于操纵和控制声波和弹性波。